随机环境下多目标设计优化问题的交互式算法

Interactive Algorithms for Optimization to Multiple-objectives Design Problems with Stochastic Environment

从通信网络和运输安排等工程问题中提出了一类多目标随机优化模型,该模型含有一个随机线性和随机二次目标函数,还含有随机线性约束.基于决策者的期望水平将多目标优化模型转化为单目标优化问题;利用新的方差期望综合法研究了此类优化问题的确定型等价类,并设计了求解这类问题的基于决策者偏好的交互式算法.数值实验表明:方差期望综合优于已有方法,它既能够反映决策者的满意度,又能够得到更稳健的最优解.

From a kind of problems such as network design and transportation scheduling,a class of stochastic multiple-objectives optimization models have been formulated,in which there are one quaduatic and one linear objective functions and several linear constraints.We converted multiple-objectives optimization problems into a single-objective optimization problem based on the expectation level of Decision-Maker.The deterministic equivalent formulation was obtained by a new approach,called hybrid method of variance and expectation.Then,an interactive algorithm was developed,which reflected the preferences of Decision-Maker.Numerical experiments showed that the proposed new method is prior to the existing method both in reflecting the satisfaction degree of Decision-Maker and in obtaining a robust solution.